Problem during variable atribution (0.000010 becomes a huge number) C language

Question

EDITED TO BE REOPENED

People, how are you doing? So, I am trying to atribute the value 0.000010 to a variable, but it becomes a very huge number, and it shouldn't be the case of overflow, due to the type. And it is important to really be 0.000010, because it is used into a condition.

In the code below, it is the varibale dif. During debug, as double, 0.000010 becomes 4.571853192736056e-315. As float, it becomes 9.99999975e-06. If I print it, after atribution, it giver me the right value (0.000010), but debug shows me thos other things.

EDIT TO HELP COMPREHENSION:

What am I supposed to do? I have a PI value calculates as the Gregory-Leibniz series (Pi = 4 -4/3 + 4/5 - 4/7 +...). Each operation (-4/3 and + 4/5, for example) are iteractions. I need to aproximate this Pi to the constant M_PI, from math.h library with a maximum difference of X (a number entered by the user). For exemple, it is necessary 100002 iteractions in the serie to aproximate Pi and M_PI with a difference of 0.000010. So, in this exemple, the user chose dif = 0.000010 and got 100002 iteractions.

The problem, as I said, is that the variable dif (as double or float) can get to be 0.000010 (DEBUG IMAGES AFTER THE CODE).

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
long int n = 0, iteractions = 0;
float Pi1 = 4.0, Pi2 = 0.0, sub = 0.0, sum = 0.0;
double dif = 0.0;

printf("Type the difference to be observed: ");
scanf("%f", &dif);

Pi1 = 4;
sub = Pi1 - M_PI;

for(n=1; sub >= dif; n++){
    Pi2 = (pow(-1,n)*4)/(2*n + 1);
    sum = Pi1 + Pi2;
    Pi1 = sum;
    sub = Pi1 - M_PI;
    iteractions = iteractions + 1;

   }
   printf("Iteractions: %ld \n", iteractions);
   return 0;
}

Image:

Answer 1

As Carcigenicate asked: What specifically is "it"? What is "it" "becoming"?

I suspect maybe you mean "iteracao" (because it's the only think you're printing), and I suspect maybe it's "huge" because the loop isn't behaving as you expect.

In any case:

1. Please read this article:

https://floating-point-gui.de/

What Every Programmer Should Know About Floating-Point Arithmetic

or

Why don’t my numbers add up?

2. Please update your post, clarifying exactly what the problem is, where in your code it's occurring, and what you "expected" vs. what you're seeing.

Answer 2

The precsion of a float is about 7 digits. You are calculating pi 3.... and want to get to within a difference of 0.000010. This is right at the limit of what a float can represent. Switching to double will give you close to 15 digits of precision.

Answer 3

You're using the wrong format specifier for scanf:

double dif = 0.0;

printf("Type the difference to be observed: ");
scanf("%f", &dif);

The %f format specifier expects a float *, but you're passing in a double *. These point to datatypes of different sizes and different representations. Using the wrong format specifier leads to undefined behavior which is why you're getting the wrong value.

To read a double, use %lf:

scanf("%lf", &dif);

Also, the value 0.000010 cannot be represented exactly in binary floating point, so even with this fix you'll see a value that is slightly larger or slightly smaller than the entered value.

Answer 4

people, thank you for the help. The right code is this one bellow.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
int n = 0, iteractions = 1;
double Pi1 = 4.0, serie = 0.0, sub = 0.0, sum = 0.0;
double dif = 0.0;

printf("Type the difference to be observed: ");
scanf("%lf", &dif);

Pi1 = 4;
sub = Pi1 - M_PI;

for(n=1; sub >= dif; n++){

    serie = (pow(-1,n)*4)/(double)(2*n + 1);

    iteractions = iteractions + 1;

    sum = Pi1 + serie;

    Pi1 = sum;

    sub = Pi1 - M_PI;

    if(sub < 0){
        sub = -1 * sub;
    }

}

printf("Iteractions: %d \n", iteractions);

return 0;
}